Introduction

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Welcome!

This website provides interactive results for the forecasting models explored in the paper Estimating Neighborhood Rents using Scraped Data.

The goal of this research is to a.) understand the temporal dynamics of rent estimates in Seattle and b.) forecast the current quarter’s rent levels based off of the prior periods. The focal series of models regress median one-bedroom rent asked values on different specifications of the panel’s correlation structure (i.e. temporal and spatial). All of the candidate models’ posterior distributions are estimated with integrated nested Laplace approximations (INLA) using the default, weakly-informative priors for all model hyperparameters. Throughout the following analyses, the training data are 2017 Q2 up to the prior quarter (i.e. 2018 Q1). The test period is a forecast for the current period and includes comparison to the appropriate median rent estimates for data observed so far in this period.

Most graphics include some level of interactivity, usually either hover-over tooltip information or a slider to control various views of the graphic. Clicking on cases will highlight data elements in most graphics, and double-clicking will reset the graphic. You can download the source code and data for this project from Github here.

Contact Chris Hess at hesscl@uw.edu for more information about this research.

This page was last updated: 2018-06-02




Table of Contents

Page Description
Distribution density graphic to investigate the distribution of rents among Seattle neighborhoods for each quarter
Panel Time-Series line graphic to show the observed or modeled temporal structure
Spatial Time-Series series of maps to show observed change across time
Model Fit tables of model root mean square error (RMSE), mean absolute error (MAE), and deviance information criterion (DIC) across training and test data

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Observed vs. Smoothed Rent Estimates

Distribution

Panel Time-Series

Spatial Time-Series

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Observed

Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)

Model Fit

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Model Legend

Model abbr. Description
int Quarter fixed intercept
log(med1B) ~ 1 + Qtr
ns Non-spatial tract random effect for each tract, quarter fixed intercept
log(med1B) ~ 1 + Qtr + f(idtract, model = “iid”)
nsar1 Non-spatial tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “iid”) + f(idqtr, model = “ar1”) + , f(idqtr1, model = “iid”)
bym Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”)
spt Spatial intrinsic conditional autoregressive (ICAR) tract random-effect, non-spatial i.i.d tract random effect, AR(1) random effect for prior quarter, i.i.d random effect for current quarter, i.i.d. random effect for tract-quarter (space-time interaction)
log(med1B) ~ 1 + f(idtract, model = “bym”, scale.model = T, graph = “../output/seatract.graph”) + , f(idqtr, model = “ar1”) + f(idqtr1, model = “iid”) + f(idtractqtr, , model = “iid”)

Accuracy and Information Criteria

train_test int_rmse ns_rmse nsar1_rmse bym_rmse spt_rmse
Test 309.0099 214.7089 206.7180 199.0735 213.0797
Training 325.0620 141.2202 141.6717 143.6970 82.5714



train_test int_mae ns_mae nsar1_mae bym_mae spt_mae
Test 254.0486 154.08054 147.61005 141.25380 153.24808
Training 260.6634 93.81771 93.98435 96.52669 54.72477



train_test int_DIC ns_DIC nsar1_DIC bym_DIC spt_DIC
Training -182.2634 -688.6591 -688.5317 -691.5972 -819.2605



train_test int_WAIC ns_WAIC nsar1_WAIC bym_WAIC spt_WAIC
Training -181.8581 -670.8105 -670.5209 -673.3005 -815.7556

Hyperparameters

Non-Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 92.9886 7.1199 79.5460 92.8120 107.5357 92.5807
Precision for idtract 30.7903 4.3235 23.0944 30.5172 40.0889 30.0053
Precision for idqtr 3040.2407 3357.8052 391.0750 2039.0533 11798.0230 987.1305
Rho for idqtr 0.2993 0.3652 -0.4779 0.3396 0.8684 0.5134
Precision for idqtr1 17174.5569 21584.3782 458.7981 10027.7571 74828.5879 826.6610



Spatial AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 92.1709 7.1077 78.8509 91.9477 106.8282 91.5688
Precision for idtract (iid component) 93.3418 24.3921 54.1954 90.4118 149.5783 84.8657
Precision for idtract (spatial component) 87.0456 28.4548 44.5954 82.6040 155.0367 74.4591
Precision for idqtr 3065.5011 3357.1731 397.2610 2065.3728 11832.9200 1003.1010
Rho for idqtr 0.3037 0.3633 -0.4713 0.3445 0.8686 0.5180
Precision for idqtr1 17931.6053 22325.7848 509.6916 10584.7825 77753.1721 958.3082



Spatiotemporal AR(1)
mean sd 0.025quant 0.5quant 0.975quant mode
Precision for the Gaussian observations 161.3434 21.2993 118.4730 160.0949 213.2248 159.5102
Precision for idtract (iid component) 92.6531 24.0910 54.1657 89.6940 148.3129 84.0927
Precision for idtract (spatial component) 87.4157 28.5263 44.4924 83.0962 155.4545 75.1241
Precision for idqtr 3064.9276 3396.1439 394.2837 2051.9623 11907.5795 994.1515
Rho for idqtr 0.3158 0.3625 -0.4633 0.3586 0.8744 0.5407
Precision for idqtr1 16225.2395 20660.7920 398.5820 9330.2530 70899.3098 675.2988
Precision for idtractqtr 220.2908 38.3304 155.4227 215.5177 313.5083 208.1564

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Non-Spatial AR(1)

Spatial AR(1)

Spatiotemporal AR(1)